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Manual 2LM-3LM V1.10
This Excel Workbook is a supplement to the paper:
Miedema, S.A. & Ramsdell, R.C., "An analysis of the hydrostatic approach of Wilson for the friction of a sliding bed". Proceedings of WEDA XXXIV Technical Conference & TAMU 45 Dredging Seminar, June 2014, Toronto, Canada. Supplemental Excel Workbook.
Please refer as above if you use any of this workbook for publications, reports or in any other way.
The input fields in green (rows 3-13) can be modified. The numbers in red (rows 20-24) are derived quantities, do not change them. The numbers in black (rows 14-19) show the progress of the calculations, do not change them.
For sand normally only the pipe diameter and the particle diameter should be modified (rows 3 and 4).
Do not change anything from column C and higher.
There are 3 switches for the 2LM/3LM model to change the modelling:
1. The bed shear stress. The Miedema (2014) method uses a Darcy-Weisbach friction factor depending on many parameters. The Televantos (1979) method multiplies the Darcy-Weisbach friction factor based on the particle diameter as the roughness with a factor between 2 and 3. The Televantos (1979) method is used by Wilson (1992) in his original model.
2. The layer model. The 2 layer model (2LM) uses a sliding bed and the water above it. But no suspension or sheet flow. This is like the original Wilson (1992) model. The 3 layer model (3LM) also uses the particle transport in the sheet flow layer, resulting in 3 layers. The particle transport in the sheet flow layer has been described by Pugh & Wilson (1999).
3. The bed-wall stress approach. The sliding bed friction force depends on the normal stress between the bed and the pipe wall. The 3 methods are described in the paper of Miedema & Ramsdell (2014). Wilson (1992) assumes a Hydrostatic wall stress. Miedema & Ramsdell (2014) added the Normal Stress approach and the Weight approach.
The suspension part is still experimental. This model is based on a threshold velocity. Below the threshold velocity there is a stationary or sliding bed with or without sheet flow. Above the threshold velocity a fraction of the solids is in suspension. This fraction increases with increasing line speed. Two methods are used to determine the threshold velocity.
1. The method of Wilson et al. (1990).
2. The method of Miedema (2013, 2014).
On top of this the hydraulic gradient can be determined weighed, by taking the bed fraction as a sliding bed model and the suspended fraction as the ELM (Equivalent Liquid Model), or limited, the hydraulic gradient cannot be smaller than the ELM hydraulic gradient. The speed with which the bed dissolves is determined by a power. Wilson uses 1.7, Miedema 2.0, but many others 1.0.
After entering the correct inputs, press the calculate button to start the calculations. This may take a few seconds depending on your computer. When the calculations are completed (row 14) goto the Graphs tab to see the results.
We believe that the Miedema & Ramsdell (2014) weight approach combined with the Miedema & Matousek (2014) bed shear stress approach is the closest to reality.
Have fun using this Workbook!
Sape Miedema & Robert Ramsdell (July 2014)
Disclaimer: This Excel workbook is free to use. The authors do not take any responsibility for the results of the calculations. This Excel workbook is for demonstation purposes and is used at your own risk.